PN functions were first introduced to construct finite projective planes by Dembowski and Ostrom [1]} in 1968.
Then looking for new non-equivalent PN functions aroused a lot of interest for many researchers in cryptography since these functions are optimally resistant to linear and differential cryptanalysis when used in DES-like cryptosystems.
Up to now, all known PN functions from \( {\mathbb {F}}_{p^m}\)  to \( {\mathbb {F}}_{p^m}\)  with explicit expressions are equivalent to one of the following
polynomials [2]}, [1]}, [4]}, [5]}, [6]}, [7]}:
